APPENDIX F

COMPOSITE VARIABLES FOR SSPS AND
ADDITIONAL COLONIES

Due to the nature of the calculations discussed in
appendix D it was
necessary to construct composites by making separate aggregates for each.
One is for the nonlabor, nonchemical processing and fabricating plant costs, and is
expressed in dollars (the dollar costs). Three of the aggregates are for
the number of man-years of labor needed at L5, on the Moon, and elsewhere
in space. The final aggregate is a charge for the amount of chemical
processing plants used at L5.

The dollar cost aggregate is the sum of three parts. These are: the
present value, with respect to the time at which the item was completed, of all future costs associated with
maintenance and operation; a capital charge for the use of any capital
other than chemical processing and fabricating plants at L5; and the
costs of the actual physical components. As a simplification,
construction is assumed to take place within a year, thus allowing
interest charges on components used in the early phases of construction
to be ignored. The error introduced (because in actuality construction,
especially in the case of colonies, takes longer than a year) is small.

A capital charge is defined as the constant amount that must be paid
every year of the life of some capital good so that the present value of
these payments is equal to the cost of the capital good. This definition
assumes that the productivity of the capital good is the same for every
year of its life. It follows that if the life of a capital good is
infinite and the real discount rate is X percent, then the capital charge
is X percent of the cost of the capital. The capital charge is higher
when the lifetime is finite but not very much higher if the lifetime is
long (30 years or more), as is the case in essentially all of the capital
in this program. In particular, for a real discount rate of 10 percent
and a lifetime of 30 years, the capital charge is 10.37 percent. As a
simplification, all of the capital charges assume an infinite lifetime.

The three labor and the chemical processing and fabricating plant
aggregates are calculated in precisely the same way as the dollar cost
aggregate, except that instead of using dollars of cost, man-years of
location specific labor or plants are substituted.

The costs of the components along with other costs are given in
table 6-13.

TABLE 6-13.- COSTS OF VARIOUS ITEMS 1

(4)Transportation for parts bought on Earth when oxygen and the 2nd-
generation shuttle system are available, 3$10^9

(5)Costs & location of labor for
construction, man-years

(6)Number of chemical processing & fabricating plants
needed 4

(7)Annual maintenance & operation costs

SSPS5

10 GW atbusbaron Earth

4.6100

0.6600

2950 at L5

1.9900

$30 million 30 man-yr not at L5, not on Moon

2nd & later colonies

10,000persons

.2595

7.3090

19,820 at L5

5.0000

6

Interlibrational transfer vehicle

500 kt/yrdelivered to L5
6

.0300

.0055

100 at L5

.0035

11 man-yr at L5

Mass catcher

Catches313 kt/yr

.0060

.0011

100 not at L5,not on Moon

.0033

13 man-yr, not on L5, not on Moon

Mass driver 7

625 kt/yr

.4507

.1367

700 on Moon

0

75 man-yr on Moon

Moon base

100 persons

.0721

.0219

25 on Moon

0

6

Lunar rectenna

448 GW atbusbar

17.4312

5.2875

2777 on Moon

0

6

Construction shacks

100 persons

.0300

.0055

25 at
constructionshack location

.0045 at L5

6

1 All costs are in 1975 dollars.2 Indicates columnar numbers referred to in text3Transportation costs from Earth to those places denoted as not at L5
and not on the Moon are assumed to be the same as transportation costs from
Earth to L5.4 In order to work at full capacity, a chemical processing and
fabricating plant requires an input of 1,000 kt of lunar rock annually.5 All costs for these items are before the effects of learning
curves have been taken into account. These effects are discussed in
appendix D. Do not overlook footnote 6 of table 6-12.6 An ILTV must start at the mass catchers with 625 kt of lunar
rock in order to deliver 500 kt to L5.7 A mass driver requires 0.12 GW to run at full capacity.

It may be expected that costs will fall with time. To simplify, all
of the component costs which enter the dollar aggregate are assumed
constant, purposely chosen somewhat lower than costs would initially be
and considerably higher than they would eventually be. Note also that all
of the components in table 6-13 are produced at least partly in space.
Besides component costs, the table also gives the direct costs for SSPS's
and second and later colonies. It is the transformation of these direct
costs into dollar costs, location-specific labor costs, and plant costs,
which gives the composite variables.

There are two SSPS composite variables; one for when oxygen is available
in space but the second generation shuttle system is not; the other for
when both are available and hence transportation costs are lower. To show
in some detail how the composite variables are made, a rough derivation
of the second of the two composite variables mentioned above is given
here.

Essentially, all of the data needed are in
table 6-13 and its footnotes.
The cost of material bought on Earth is, from column 3, $4.61 billion. This includes $1.01 billion for the
rectenna on Earth. The transportation cost of the material bought on
Earth is, according to column 4, $0.66 billion. The annual nonlabor costs
for maintenance and operation are, as stated in column 7, equal to $30
million. The present value at the time of construction of this, assuming
as an approximation an infinite lifetime for the SSPS's, is $0.3 billion.
Total dollar costs thus far are $5.57 billion.

Column 5 shows that the direct labor costs are 2950 man-years, all at
L5. Labor costs of maintenance and operation are obtained (as in the case
of the nonlabor costs) from the present value by multiplying the annual
figure by 10. This gives 300 workers at a location other than L5 or the
Moon. To be precise, the 300 are at geosynchronous orbit where the people
attend to the SSPS once it is in operation. The cost of the housing
accommodations for the workers at L5 is not included in the composite
variable. This is dealt with by the methodology described in appendix D.
Workers not at L5 have their housing costs counted into the variable. The
300 geosynchronous orbit workers are assumed to live in construction
shacks. From the information provided in table 6-13, this costs $0.09
billion for parts bought on Earth, $0.0165 billion for transportation, 75
man-years at geosynchronous orbit, and 0.0135 of a chemical processing
and fabricating plant.

Transportation costs from Earth to every place of relevance for these
calculations are assumed to be the same as the costs from Earth to L5.
Taking 10 percent of all of the costs of construction shacks given above
in order to obtain the appropriate capital charges gives $0.0107 billion,
8 man-years, and 0.00135 plants. The 8 man-years require housing, and the
0.00135 plants require lunar rock as input. The costs of these are small
enough to ignore. Everything is now included within the SSPS aggregate
except for a direct chemical processing and fabricating plant capital
charge of 0.199 plants and 11990 kt of lunar rock needed as input to
these plants.

To get the lunar rock within a year requires 4.0 interlibrational
transfer vehicles (ILTVs). From table 6-13, the capital charges for these
are: $0.0142 billion for parts bought on Earth and transportation, 40
man-years at L5 for construction, 0.0014 plants, and a negligible amount
of lunar rock. In addition, annual maintenance and operations costs are
44 man-years at L5. The present value of this is 440 man-years, and the
capital charge, which is the relevant number, is 44 man-years. Twenty
percent of the mass coming off the Moon is used as fuel for the ILTVs.
Thus, 2488 kt are needed from the
Moon. To catch it, 8.0 mass catchers are needed. The resulting charges
are $0.0057 billion, 184 man-years not at L5 or on the Moon, 0.00264 plants, and negligible lunar rock. The 184
man-years of labor are derived from workers housed in construction shacks
for which is charged $0.0065 billion, 5 man-years which are not at L5 or
on the Moon, and 0.00083 plants.

On the Moon 4.0 mass drivers are required. The charges for these are
$0.235 billion and 580 man-years on the Moon. All of the plants discussed
thus far were at L5. Their costs are converted to dollar costs by the
algorithm given in appendix D. The costs of the plants on the Moon are
measured in terms of dollars needed to purchase parts on Earth and the
dollars needed to pay for the transportation of these parts to the Moon.
These dollar costs are included in the amounts given in columns 3 and 4
of table 6-13.

The power used by 4.0 mass drivers is 0.48 GW. This is 0.1071 of the
4.48 GW that an SSPS with lunar rectenna can deliver. The capital charge
for this fraction of a rectenna is $0.2433 billion and 30 man-years on
the Moon. Thus far, there is a total lunar labor charge of 610 man-years.
The capital charge for the lunar base additions that these people require
is $0.0573 billion and 15 man-years of labor on the Moon.

One final item is needed: 0.1071 of an SSPS beaming power to the Moon.
The costs of such an SSPS are the same as the costs of the SSPS being
evaluated, except that the $1.01 billion for a rectenna on Earth need not
be paid. Thus, building one SSPS requires 0.1071 of a second SSPS plus
(0.1071)^2 of a third SSPS plus (0.1071)^3 of a fourth, and so on. The sum
of this series is 1.1199. Therefore multiplying all the previous costs by
1.1199 and subtracting $0.1211 billion for the Earth-based rectenna
correction gives the final result of a cost of $6.76 billion, 3398
man-years at L5, 700 on the Moon, 557 not at L5 or the Moon, and 0.2298
chemical processing and fabricating plants.

These costs of the SSPS variable are for when both oxygen in space and
the second-generation shuttle are available. To obtain the costs of the
SSPS variable when only oxygen is available, the transportation costs
given in column 4 of table 6-13 are adjusted in accordance with the
information given in table 6-10. The result is a cost of $9.73 billion
with the nondollar costs remaining the same.

Colony composite variable costs are found by a similar method. A
somewhat rougher calculation than that for the SSPS yields $9.24 billion,
20,946 man-years at L5, 1759 on the Moon, and 626 elsewhere. From
table 6-13 it is seen that the direct dollar costs are $7.57 billion. This
direct cost may be broken down as follows: plants and animals cost,
including transportation, $0.68 billion; nitrogen in the atmosphere and H
2
for H2O cost, including transportation, $2.42 billion; high technology
equipment from Earth and personal belongings cost, $2.88 billion.
Finally, $1.6 billion is needed to pay for transportation for 10,000
colonists.